Let us now turn to the 2-body twist-3 contribution to the subprocess amplitudes. It is tightly
connected to the 3-body twist-3 contribution through the equations of motion (EOMs).
In fact, for light-cone gauge which we have chosen for the vacuum-pion matrix element (more details on that
choice for the twist-3 calculation have been given in [1]}),
the 2-body twist-3 DAs are related to the 3-body one, \(\phi _{3\pi }(\tau _a,\tau _b,\tau _g)\) ,
integrated upon the momentum fraction the constituent gluon carries:
\(\tau \phi _{\pi p}(\tau ) + \frac{\tau }{6}\, \phi ^{\prime }_{\pi \sigma }(\tau ) - \frac{1}{3}\, \phi _{\pi \sigma }(\tau )& = & \phi ^{EOM}_{\pi 2} (\bar{\tau })\,, \nonumber \\\bar{\tau } \phi _{\pi p}(\tau ) - \frac{\bar{\tau }}{6} \phi ^{\prime }_{\pi \sigma }(\tau ) -\frac{1}{3} \phi _{P\sigma }(\tau )& = & \phi ^{EOM}_{\pi 2} (\tau )\,,\) 
